On the (v,5, )-Family of Bhaskar Rao Designs

We establish that the necessary conditions for the existence of Bhaskar Rao designs of block size ve are : i). (v 1) 0 (mod 4) ii). v(v 1) 0 (mod 40) iii). 2j. We show these conditions are suucient: for = 4 if v > 215, with 10 smaller possible exceptions and one deenite exception at v = 5; for = 10 if v > 445, with 11 smaller possible exceptions, and one deenite exception at v = 5; and for = 20, with the possible exception of v = 32; we also give a few results for other values of .